Ack-Ack....... In some areas, it's a good idea to hesitate as per your statement (and I quote) "this is exactly why I did not just want to just whack the puller bolt as a matter of course."....
I've seen the reasoning for that statement in various manuals also, however smacking the top of that puller with the biggest hammer in your tool box is normally the only action that is going to break the flywheel taper away from the crankshaft... and you can take it from one (or more) who has been down that road a few hundred times or so.
Also, the 40hp is one among a few other models that is notorious (usually) in having the demon from Hell associated with it that is assigned to associate having that flywheel practically welded to the crankshaft... other models include the 28hp and 33hp models that incorporate the 311356 crankshaft. A few of these have necessitated the old wives tale of prying up the flywheel slightly to relieve the slight play available... actually reliving that play allows the flywheel/crankshaft a bit more room to separate from the puller (Or Something!)... it does make a difference. That slight bit of prying has saved the day for me a few times.
So... first shot is to tighten the puller as much as possible. If that doesn't have the flywheel breaking free... second shot is to re-tighten and get out the big hammer... third shot is the big hammer and the pry-bar, large screwdriver, whatever... fourth shot would be to excessively tighten the puller and spray penetrating oil on the crankshaft top area and wait, and wait and wait!... the fifth and final shot is to remove the power-head and make a trip to a reliable machine shop.... and you polish off a six pack!
Whatever you do, don't be tempted to apply heat to it as that will cause warpage of the flywheel quite quickly.